library(tidyverse)
library(knitr)
library(sjPlot)
library(gridExtra)
library(lme4)
library(emmeans)
library(car) # for vif
library(bbmle) # for AICtab
library(broom) # for glance
theme_set(ggthemes::theme_few())

Summary

Mixed modeling with all relevant variables predicting accuracy

From the preregistration, the mixed model was specified thusly:

correct ~ delay * age + 
          task_experience + cup_distance + board_size + trial +
          (1 + delay + trial | site/subject/block/hiding_location ) + 
          (1 + task_experience + cup_distance + board_size + trial + delay | species)

In the dataframe, subject_site = subject, and norm_age should be used for age.

Model as pre-registered has too many random effects

Error: number of observations (=6246) < number of random effects (=10608) for term (1 + delay + trial | hiding_location:(block:(subject_site:site))); the random-effects parameters are probably unidentifiable

Pruning random effects in the following order (from preregistration):

  • Remove correlations between random effects
  • Remove random slopes (in the following order)
    • species
    • hiding_location
    • block
    • subject

Model only converges once we take out hiding_location. After doing so, the other random effects (correlation, site, species) can be put back in.

The model below converges. Model output is saved in 06_mp_model_v2.rds

correct ~ delay * norm_age + 
          task_experience + cup_distance + board_size + trial + 
          (1 + delay + trial | site/subject_site) + 
          (1 + task_experience + cup_distance + board_size + trial + delay | species)

Reduced model

After pruning random effects with little variability and removing board_size, which covaried with cup_distance, the reduced model has the following structure. It is saved in 06_mp_3_model3_v2.rds

correct ~ delay * norm_age + 
          task_experience + cup_distance + trial + 
          (1 + delay | site/subject_site) + 
          (1 + delay | species)

Data prep

Data import

mp_data <- read.csv("../data/merged_data/01_manyprimates_pilot_merged_data_v2.csv")

Prepare code for pre-registered mixed modeling

  • center cup_distance, board_size and trial
  • filter out spider monkey. Only one data point so far, therefore this is not worth including to explode the number of random effects
model.data <- mp_data %>%
  filter(species != "black_faced_spider_monkey") %>%
  mutate_at(vars(cup_distance, board_size, trial), funs(scale(.)[, 1])) %>%
  mutate(hiding_location = factor(hiding_location),
         delay = fct_relevel(delay, "short"))

Model 1

The model takes a while to run. Run next line to load model output from previous run with structure below.

mm.1 <- glmer(correct ~ delay * norm_age +
               task_experience + cup_distance + board_size + trial +
               (1 + delay + trial | site/subject_site/block) +
               (1 + task_experience + cup_distance + board_size + trial + delay | species)
             , data = model.data
             , family = binomial
             , control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
             )

saveRDS(mm.1, "06_mp_model_v2.rds")

Some diagnostics

  • examining Cholesky decomposition
theta <- getME(mm.1, "theta")
diag.element <- getME(mm.1, "lower") == 0
any(theta[diag.element] < 1e-5)

Model summary

Confirm model structure

# mm.1@call
formula(mm.1)
correct ~ delay * norm_age + task_experience + cup_distance + 
    board_size + trial + (1 + delay + trial | site/subject_site) + 
    (1 + task_experience + cup_distance + board_size + trial + 
        delay | species)
glance(mm.1) %>% kable(digits = 2)

Random effects

VarCorr(mm.1) %>% print(formatter = fmt, digits = 3) # comp = c("Variance", "Std.Dev.")
 Groups            Name               Std.Dev. Corr                         
 subject_site:site (Intercept)        0.862                                 
                   delaylong          0.646    -0.91                        
                   delaymedium        0.528    -0.85  0.99                  
                   trial              0.093    -0.31  0.61  0.71            
 site              (Intercept)        0.917                                 
                   delaylong          0.512    -1.00                        
                   delaymedium        0.627    -1.00  1.00                  
                   trial              0.084     1.00 -1.00 -1.00            
 species           (Intercept)        0.835                                 
                   task_experienceyes 0.173    -1.00                        
                   cup_distance       0.012     1.00 -1.00                  
                   board_size         0.232    -1.00  1.00 -1.00            
                   trial              0.021    -1.00  1.00 -1.00  1.00      
                   delaylong          0.494    -1.00  1.00 -1.00  1.00  1.00
                   delaymedium        0.436    -1.00  1.00 -1.00  1.00  1.00
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
  1.00

Fixed effects

CIs

mm.1.ci <- confint(mm.1, method = "Wald") %>% # bootstrap these later
  as.data.frame %>%
  rownames_to_column %>%
  filter(complete.cases(.)) %>%
  rename(LL = `2.5 %`, UL = `97.5 %`) %>%
  mutate(OR_LL = exp(LL), OR_UL = exp(UL))
coef(summary(mm.1)) %>%
  as.data.frame %>%
  rownames_to_column() %>%
  mutate(OR = exp(Estimate)) %>%
  left_join(mm.1.ci, by = "rowname") %>%
  select(rowname, OR, OR_LL, OR_UL, Estimate, LL, UL, everything()) %>%
  kable(digits = 3)
corr <- cov2cor(vcov(mm.1)) %>% as.matrix %>% round(2)
corr[upper.tri(corr, diag = T)] <- ""
colnames(corr) <- 1:10
rownames(corr) <- str_c(1:10, " ", rownames(corr))

corr %>% as.data.frame %>% select(-10) %>% rownames_to_column

Pairwise contrasts for delay

based on estimated marginal means

Note. This wasn’t in the preregistration.

emmeans(mm.1, pairwise ~ delay, type = "response")$contrasts
 contrast       odds.ratio         SE  df z.ratio p.value
 short / long    3.5160746 0.92828519 Inf   4.762  <.0001
 short / medium  2.7103806 0.75716209 Inf   3.569  0.0010
 long / medium   0.7708541 0.07335892 Inf  -2.735  0.0172

Results are averaged over the levels of: task_experience 
P value adjustment: tukey method for comparing a family of 3 estimates 
Tests are performed on the log odds ratio scale 

Model 1 plots

Fixed effects

plot_model(mm.1, title = "Fixed Effects", order.terms = c(7, 4, 3:1, 9:8, 5, 6),
           width = .3, show.values = T, value.size = 2.5, value.offset = .3) +
  geom_hline(yintercept = 1, lty = 2) +
  ylim(0, 3)

Random effects

Subject/Site

ranef.plots[[1]]

Site

Species


Pruning the model

  • remove trial random slopes within species as the estimates in the previous models were essentially 0
correct ~ delay * norm_age + 
          task_experience + cup_distance + board_size + trial +
          (1 + delay + trial | site/subject_site ) +         
          (1 + task_experience + cup_distance + board_size + delay | species)

Check colinearity in the previous model

vif(col.mm1)
                    GVIF Df GVIF^(1/(2*Df))
delay           1.007876  2        1.001963
norm_age        1.072757  1        1.035740
task_experience 1.056383  1        1.027805
cup_distance    1.323990  1        1.150648
board_size      1.296698  1        1.138726
trial           1.001067  1        1.000533

No signs of high colinaearity.

Check levels of random effects

Check how many different levels there are within each random effect

overview$summary
$`delay_within_species (factor)`

 3 
11 

$`task_experience_within_species (factor)`

1 2 
9 2 

$`board_size_within_species (covariate)`

1 2 4 
5 5 1 

$`cup_distance_within_species (covariate)`

1 2 4 
6 4 1 

$`trial_within_species (covariate)`

36 
11 

This suggests that, within species, random slopes for task_experience does not make much sense as most species have only 1 level. Same is true for cup_distance and board_size. Indeed, the model summary and random effects plot for species confirm that there is little variability in these estimates (they’re close to zero). Therefore they are removed.

correct ~ delay * norm_age + 
          task_experience + cup_distance + board_size + trial +
          (1 + delay + trial | site/subject_site ) +         
          (1 + delay | species)

Model 2

The model takes a while to run. Run next line to load model output from previous run with structure below.

mm.2 <- readRDS("06_2_mp_model2_v2.rds")
# mm.2.ci <- readRDS("06_2_mp_model2_ci_v2.rds")
mm.2 <- glmer(correct ~ delay * norm_age +
              task_experience + cup_distance + board_size + trial +
              (1 + trial + delay | site/subject_site) +
              (1 + delay | species)
              , data = model.data
              , family = binomial
              , control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
              )

saveRDS(mm.2, "06_2_mp_model2_v2.rds")

Model 3

Remove trial from the random slopes for subject/site as it’s near zero both in mm.1 and even more so in mm.2

VarCorr(mm.2) %>% print(comp = c("Variance", "Std.Dev."), formatter = fmt, digits = 3)
 Groups            Name        Variance Std.Dev. Corr             
 subject_site:site (Intercept) 0.74     0.86                      
                   trial       0.009    0.093    -0.29            
                   delaylong   0.417    0.646    -0.91  0.60      
                   delaymedium 0.279    0.528    -0.85  0.69  0.99
 site              (Intercept) 1.052    1.026                     
                   trial       0.008    0.089     0.88            
                   delaylong   0.349    0.591    -1.00 -0.88      
                   delaymedium 0.471    0.686    -1.00 -0.89  1.00
 species           (Intercept) 0.576    0.759                     
                   delaylong   0.246    0.496    -1.00            
                   delaymedium 0.183    0.428    -1.00  1.00      

The model takes a while to run. Run next line to load model output from previous run with structure below.

mm.3 <- readRDS("06_3_mp_model3_v2.rds")
mm.3 <- glmer(correct ~ delay * norm_age +
              task_experience + cup_distance + board_size  + trial +
              (1 + delay | site/subject_site) +
              (1 + delay | species)
              , data = model.data
              , family = binomial
              , control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
              )

saveRDS(mm.3, "06_3_mp_model3_v2.rds")

Model summary

Confirm model structure

formula(mm.3)
correct ~ delay * norm_age + task_experience + cup_distance + 
    board_size + trial + (1 + delay | site/subject_site) + (1 + 
    delay | species)
glance(mm.3) %>% kable(digits = 2)

LRT

drop1(mm.3, test = 'Chisq')
Single term deletions

Model:
correct ~ delay * norm_age + task_experience + cup_distance + 
    trial + (1 + delay | site/subject_site) + (1 + delay | species)
                Df    AIC     LRT  Pr(Chi)    
<none>             6836.2                     
task_experience  1 6834.4  0.1483   0.7001    
cup_distance     1 6854.5 20.3087 6.59e-06 ***
trial            1 6835.0  0.7541   0.3852    
delay:norm_age   2 6832.6  0.3836   0.8255    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Random effects

VarCorr(mm.3) %>% print(comp = c("Variance", "Std.Dev."), formatter = fmt, digits = 3)

Fixed effects

CIs

# this is not currently run
source("boot_glmm.r")

mm.3.ci <- boot.glmm.pred(model.res = mm.3, excl.warnings = F, nboots = 1000,
                         para = F, resol = 100, level = 0.95, use = NULL,
                         circ.var.name = NULL, circ.var = NULL, use.u = F,
                         n.cores = c("all-1", "all"), save.path = NULL)

saveRDS(mm.3.ci, "06_3_mp_model3_ci_v2.rds")
mm.3.ci <- confint(mm.3, method = "Wald") %>% # bootstrap these later
  as.data.frame %>%
  rownames_to_column %>%
  filter(complete.cases(.)) %>%
  rename(LL = `2.5 %`, UL = `97.5 %`) %>%
  mutate(OR_LL = exp(LL), OR_UL = exp(UL))
coef(summary(mm.3)) %>%
  as.data.frame %>%
  rownames_to_column() %>%
  mutate(OR = exp(Estimate)) %>%
  left_join(mm.3.ci, by = "rowname") %>%
  select(rowname, OR, OR_LL, OR_UL, Estimate, LL, UL, everything()) %>%
  kable(digits = 3)

Pairwise contrasts for delay

based on estimated marginal means

(emm <- emmeans(mm.3, pairwise ~ delay)$contrasts)
 contrast         estimate        SE  df z.ratio p.value
 short - long    1.4257372 0.2800475 Inf   5.091  <.0001
 short - medium  1.1604769 0.2810297 Inf   4.129  0.0001
 long - medium  -0.2652602 0.0865917 Inf  -3.063  0.0062

Results are averaged over the levels of: task_experience 
Results are given on the log odds ratio (not the response) scale. 
P value adjustment: tukey method for comparing a family of 3 estimates 
confint(emm)
 contrast         estimate        SE  df  asymp.LCL   asymp.UCL
 short - long    1.4257372 0.2800475 Inf  0.7693896  2.08208469
 short - medium  1.1604769 0.2810297 Inf  0.5018275  1.81912636
 long - medium  -0.2652602 0.0865917 Inf -0.4682053 -0.06231523

Results are averaged over the levels of: task_experience 
Results are given on the log odds ratio (not the response) scale. 
Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 3 estimates 
(emm.or <- emmeans(mm.3, pairwise ~ delay, type = "response")$contrasts)
 contrast       odds.ratio         SE  df z.ratio p.value
 short / long    4.1609240 1.16525642 Inf   5.091  <.0001
 short / medium  3.1914550 0.89689360 Inf   4.129  0.0001
 long / medium   0.7670063 0.06641638 Inf  -3.063  0.0062

Results are averaged over the levels of: task_experience 
P value adjustment: tukey method for comparing a family of 3 estimates 
Tests are performed on the log odds ratio scale 
confint(emm.or)

Model 3 plots

Fixed effects

ggsave("../graphs/05_forestplot.png", fe.3, width = 3, height = 2.5, scale = 2)

Random effects

Subject/Site

ranef.plots2[[1]]

Site

ranef.plots2[[2]]

Species

Model 4

  • further remove subject/site random effects to look at species differences (from preregistration)

Random effects

plot.data <- get_model_data(mm.4, type = "re", show.values = T) %>%
  left_join(phylo, by = c("term" = "species")) %>%
  rename(species = species_formatted) %>%
  mutate(
    facet = fct_rev(facet),
    facet = fct_recode(facet, "Intercept" = "species (Intercept)",
                       "Delay (short vs. long)" = "delaylong", 
                       "Delay (short vs. medium)" = "delaymedium")
    )
Column `term`/`species` joining factor and character vector, coercing into character vector

Model comparison

We’re looking for the lowest AIC(c) as the model with the ‘best fit’ with a reasonable number of parameters. (Too many are penalized by AIC as one way to address overfitting.)

Indeed, the reduced model seems to do a better job of striking that balance between fitting the data with fewer parameters.

AICctab(mm.1, mm.2, mm.3, mm.4, logLik = T, weights = T)
     dLogLik dAICc df weight
mm.3 109.9     0.0 28 0.9982
mm.2 111.6    12.7 36 0.0018
mm.1 112.9    54.9 58 <0.001
mm.4   0.0   193.6 15 <0.001
anova(mm.1, mm.2, mm.3, mm.4)
Data: model.data
Models:
mm.4: correct ~ delay * norm_age + task_experience + cup_distance + 
mm.4:     trial + (1 + delay | species)
mm.3: correct ~ delay * norm_age + task_experience + cup_distance + 
mm.3:     board_size + trial + (1 + delay | site/subject_site) + (1 + 
mm.3:     delay | species)
mm.2: correct ~ delay * norm_age + task_experience + cup_distance + 
mm.2:     board_size + trial + (1 + trial + delay | site/subject_site) + 
mm.2:     (1 + delay | species)
mm.1: correct ~ delay * norm_age + task_experience + cup_distance + 
mm.1:     board_size + trial + (1 + delay + trial | site/subject_site) + 
mm.1:     (1 + task_experience + cup_distance + board_size + trial + 
mm.1:         delay | species)
     Df    AIC    BIC  logLik deviance    Chisq Chi Df Pr(>Chisq)    
mm.4 15 7032.3 7133.4 -3501.1   7002.3                               
mm.3 28 6838.5 7027.2 -3391.3   6782.5 219.7490     13     <2e-16 ***
mm.2 36 6851.0 7093.6 -3389.5   6779.0   3.5119      8     0.8983    
mm.1 58 6892.6 7283.5 -3388.3   6776.6   2.4403     22     1.0000    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Difference in regression coefficients

Difference

coef2 - coef1
   delaylong  delaymedium cup_distance 
 -0.16840056  -0.16341754  -0.06131301 

Difference in odds ratios

exp(coef2) - exp(coef1)
   delaylong  delaymedium cup_distance 
 -0.04407273  -0.05561161  -0.09242183 
---
title: "ManyPrimates pilot mixed modeling"
author: "Drew Altschul"
date: "18 Oct 2018"
output:
  html_notebook:
    css: style.css
    theme: paper
    toc: yes
    toc_float: yes
---

```{r setup, message=FALSE}
library(tidyverse)
library(knitr)
library(sjPlot)
library(gridExtra)
library(lme4)
library(emmeans)
library(car) # for vif
library(bbmle) # for AICtab
library(broom) # for glance

theme_set(ggthemes::theme_few())
```

# Summary

Mixed modeling with all relevant variables predicting accuracy

From the preregistration, the mixed model was specified thusly:

```
correct ~ delay * age + 
          task_experience + cup_distance + board_size + trial +
          (1 + delay + trial | site/subject/block/hiding_location ) + 
          (1 + task_experience + cup_distance + board_size + trial + delay | species)
```

In the dataframe, 
`subject_site = subject`,
and `norm_age` should be used for `age`.

Model as pre-registered has too many random effects

```
Error: number of observations (=6246) < number of random effects (=10608) for term (1 + delay + trial | hiding_location:(block:(subject_site:site))); the random-effects parameters are probably unidentifiable
```

Pruning random effects in the following order (from preregistration): 

> - Remove correlations between random effects
> - Remove random slopes (in the following order)
>     - `species`
>     - `hiding_location`
>     - `block`
>     - `subject`

Model only converges once we take out `hiding_location`. After doing so, the other random effects (correlation, site, species) can be put back in.

The model below converges. Model output is saved in `06_mp_model_v2.rds`

```
correct ~ delay * norm_age + 
          task_experience + cup_distance + board_size + trial + 
          (1 + delay + trial | site/subject_site) + 
          (1 + task_experience + cup_distance + board_size + trial + delay | species)
```

## Reduced model

After pruning random effects with little variability and removing `board_size`, which covaried with `cup_distance`, the reduced model has the following structure. It is saved in `06_mp_3_model3_v2.rds`

```
correct ~ delay * norm_age + 
          task_experience + cup_distance + trial + 
          (1 + delay | site/subject_site) + 
          (1 + delay | species)
```

![](../graphs/05_forestplot.png)

***

# Data prep

Data import

```{r loading data}
mp_data <- read.csv("../data/merged_data/01_manyprimates_pilot_merged_data_v2.csv")
```

Prepare code for pre-registered mixed modeling

- center `cup_distance`, `board_size` and `trial`
- filter out spider monkey. Only one data point so far, therefore this is not worth including to explode the number of random effects

```{r}
model.data <- mp_data %>%
  filter(species != "black_faced_spider_monkey") %>%
  mutate_at(vars(cup_distance, board_size, trial), funs(scale(.)[, 1])) %>%
  mutate(hiding_location = factor(hiding_location),
         delay = fct_relevel(delay, "short"))
```

# Model 1

The model takes a while to run. Run next line to load model output from previous run with structure below.

```{r}
# mm.1 <- readRDS("06_mp_model.rds")
mm.1 <- readRDS("06_mp_model_v2.rds")
```

```{r, eval=FALSE}
mm.1 <- glmer(correct ~ delay * norm_age +
               task_experience + cup_distance + board_size + trial +
               (1 + delay + trial | site/subject_site/block) +
               (1 + task_experience + cup_distance + board_size + trial + delay | species)
             , data = model.data
             , family = binomial
             , control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
             )

saveRDS(mm.1, "06_mp_model_v2.rds")
```

Some diagnostics

- examining Cholesky decomposition

```{r}
theta <- getME(mm.1, "theta")
diag.element <- getME(mm.1, "lower") == 0
any(theta[diag.element] < 1e-5)
```

## Model summary

Confirm model structure

```{r}
# mm.1@call
formula(mm.1)
```

```{r, results="asis"}
glance(mm.1) %>% kable(digits = 2)
```

## Random effects

```{r}
fmt <- function(num, digits) return(round(num, digits))
VarCorr(mm.1) %>% print(formatter = fmt, digits = 3) # comp = c("Variance", "Std.Dev.")
```

## Fixed effects

CIs

```{r}
mm.1.ci <- confint(mm.1, method = "Wald") %>% # bootstrap these later
  as.data.frame %>%
  rownames_to_column %>%
  filter(complete.cases(.)) %>%
  rename(LL = `2.5 %`, UL = `97.5 %`) %>%
  mutate(OR_LL = exp(LL), OR_UL = exp(UL))
```

```{r, results="asis"}
coef(summary(mm.1)) %>%
  as.data.frame %>%
  rownames_to_column() %>%
  mutate(OR = exp(Estimate)) %>%
  left_join(mm.1.ci, by = "rowname") %>%
  select(rowname, OR, OR_LL, OR_UL, Estimate, LL, UL, everything()) %>%
  kable(digits = 3)
```

<!-- ## Correlation of Fixed Effects -->

```{r, eval=FALSE, results="asis"}
corr <- cov2cor(vcov(mm.1)) %>% as.matrix %>% round(2)
corr[upper.tri(corr, diag = T)] <- ""
colnames(corr) <- 1:10
rownames(corr) <- str_c(1:10, " ", rownames(corr))

corr %>% as.data.frame %>% select(-10) %>% rownames_to_column
```

## Pairwise contrasts for delay

based on estimated marginal means

*Note. This wasn't in the preregistration.*

```{r, message=FALSE}
emmeans(mm.1, pairwise ~ delay, type = "response")$contrasts
```

# Model 1 plots

## Fixed effects

```{r, fig.width=4, fig.height=2.5, message=FALSE}
plot_model(mm.1, title = "Fixed Effects", order.terms = c(7, 4, 3:1, 9:8, 5, 6),
           width = .3, show.values = T, value.size = 2.5, value.offset = .3) +
  geom_hline(yintercept = 1, lty = 2) +
  ylim(0, 3)
```

## Random effects

```{r}
ranef.plots <- plot_model(mm.1, type = "re", sort.est = "(Intercept)")
```

### Subject/Site

```{r fig.height=20, fig.width=10}
ranef.plots[[1]]
```

### Site

```{r, fig.width=10, fig.height=8}
ranef.plots[[2]]
```

### Species

```{r, fig.width=10, fig.height=3}
ranef.plots[[3]]
```

***

# Pruning the model

- remove `trial` random slopes within `species` as the estimates in the previous models were essentially 0

```
correct ~ delay * norm_age + 
          task_experience + cup_distance + board_size + trial +
          (1 + delay + trial | site/subject_site ) +         
          (1 + task_experience + cup_distance + board_size + delay | species)
```

## Check colinearity in the previous model

```{r}
col.mm1 <- glm(correct ~ delay + norm_age +
                 task_experience + cup_distance + board_size + trial
               , data = model.data
               , family = binomial)

vif(col.mm1)
```

No signs of high colinaearity.

## Check levels of random effects

Check how many different levels there are within each random effect

```{r}
source("diagnostic_fcns.r")

overview <- fe.re.tab("correct ~ delay + task_experience + board_size + cup_distance + trial", "species", data = model.data)

overview$summary
```

This suggests that, within species, random slopes for `task_experience` does not make much sense as most species have only 1 level. Same is true for `cup_distance` and `board_size`. Indeed, the model summary and random effects plot for `species` confirm that there is little variability in these estimates (they're close to zero). Therefore they are removed.

```
correct ~ delay * norm_age + 
          task_experience + cup_distance + board_size + trial +
          (1 + delay + trial | site/subject_site ) +         
          (1 + delay | species)
```

# Model 2

The model takes a while to run. Run next line to load model output from previous run with structure below.

```{r}
mm.2 <- readRDS("06_2_mp_model2_v2.rds")
# mm.2.ci <- readRDS("06_2_mp_model2_ci_v2.rds")
```

```{r, eval=FALSE}
mm.2 <- glmer(correct ~ delay * norm_age +
              task_experience + cup_distance + board_size + trial +
              (1 + trial + delay | site/subject_site) +
              (1 + delay | species)
              , data = model.data
              , family = binomial
              , control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
              )

saveRDS(mm.2, "06_2_mp_model2_v2.rds")
```

# Model 3

Remove `trial` from the random slopes for subject/site as it's near zero both in `mm.1` and even more so in `mm.2`

```{r}
VarCorr(mm.2) %>% print(comp = c("Variance", "Std.Dev."), formatter = fmt, digits = 3)
```

```{r, fig.width=10, fig.height=8}
plot_model(mm.2, type = "re", sort.est = "(Intercept)")[[1]]
```

```{r, fig.width=10, fig.height=3}
plot_model(mm.2, type = "re", sort.est = "(Intercept)")[[2]]
```

The model takes a while to run. Run next line to load model output from previous run with structure below.

```{r}
mm.3 <- readRDS("06_3_mp_model3_v2.rds")
```

```{r, eval=FALSE}
mm.3 <- glmer(correct ~ delay * norm_age +
              task_experience + cup_distance + board_size  + trial +
              (1 + delay | site/subject_site) +
              (1 + delay | species)
              , data = model.data
              , family = binomial
              , control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
              )

saveRDS(mm.3, "06_3_mp_model3_v2.rds")
```

## Model summary

Confirm model structure

```{r}
formula(mm.3)
```

```{r, results="asis"}
glance(mm.3) %>% kable(digits = 2)
```

## LRT

```{r, eval=FALSE}
drop1(mm.3, test = 'Chisq')
```

```
Single term deletions

Model:
correct ~ delay * norm_age + task_experience + cup_distance + 
    trial + (1 + delay | site/subject_site) + (1 + delay | species)
                Df    AIC     LRT  Pr(Chi)    
<none>             6836.2                     
task_experience  1 6834.4  0.1483   0.7001    
cup_distance     1 6854.5 20.3087 6.59e-06 ***
trial            1 6835.0  0.7541   0.3852    
delay:norm_age   2 6832.6  0.3836   0.8255    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
```


## Random effects

```{r}
VarCorr(mm.3) %>% print(comp = c("Variance", "Std.Dev."), formatter = fmt, digits = 3)
```

## Fixed effects

CIs

<!-- Bootstrap function by Roger Mundry @ MPI EVA -->

```{r, eval=FALSE}
# this is not currently run
source("boot_glmm.r")

mm.3.ci <- boot.glmm.pred(model.res = mm.3, excl.warnings = F, nboots = 1000,
                         para = F, resol = 100, level = 0.95, use = NULL,
                         circ.var.name = NULL, circ.var = NULL, use.u = F,
                         n.cores = c("all-1", "all"), save.path = NULL)

saveRDS(mm.3.ci, "06_3_mp_model3_ci_v2.rds")
```

```{r}
mm.3.ci <- confint(mm.3, method = "Wald") %>% # bootstrap these later
  as.data.frame %>%
  rownames_to_column %>%
  filter(complete.cases(.)) %>%
  rename(LL = `2.5 %`, UL = `97.5 %`) %>%
  mutate(OR_LL = exp(LL), OR_UL = exp(UL))
```

```{r, results="asis"}
coef(summary(mm.3)) %>%
  as.data.frame %>%
  rownames_to_column() %>%
  mutate(OR = exp(Estimate)) %>%
  left_join(mm.3.ci, by = "rowname") %>%
  select(rowname, OR, OR_LL, OR_UL, Estimate, LL, UL, everything()) %>%
  kable(digits = 3)
```

## Pairwise contrasts for delay

based on estimated marginal means

```{r, message=FALSE}
(emm <- emmeans(mm.3, pairwise ~ delay)$contrasts)
```

```{r}
confint(emm)
```

```{r, message=FALSE}
(emm.or <- emmeans(mm.3, pairwise ~ delay, type = "response")$contrasts)
```

```{r, message=FALSE}
confint(emm.or)
```


# Model 3 plots

## Fixed effects

```{r, fig.width=4, fig.height=2.5, message=FALSE}
fe.3 <- plot_model(mm.3, title = "A. Fixed Effects", axis.labels = c("Trial", "Task Experience (yes)","Board Size (cm)", "Cup Distance (cm)", "Normed Age x Delay\n(short vs. medium)", "Normed Age x Delay\n(short vs. long)", "Normed Age", "Delay (short vs. long)", "Delay (short vs. medium)"), wrap.labels = F,
                  order.terms = c(2:1,3,8:9,5,6,4, 7),
           width = .3, show.values = T, value.size = 2.5, value.offset = .3) +
  facet_wrap(~ "") +
  # geom_hline(yintercept = 1, lty = 2) +
  # annotate("label", label = "A", x = 8, y = .11, size = 5) +
  scale_y_continuous(trans = "log", limits = c(.1, 5.5), breaks = c(.1, .2, .5, 1, 2, 5))

fe.3 + theme(plot.margin = unit(c(.5, 7, .5, .5), "cm"))
```

```{r, eval = FALSE}
ggsave("../graphs/05_forestplot.png", fe.3, width = 3, height = 2.5, scale = 2)
```

## Random effects

```{r}
ranef.plots2 <- plot_model(mm.3, type = "re", sort.est = "(Intercept)")
```

### Subject/Site

```{r, fig.width=10, fig.height=8}
ranef.plots2[[1]]
```

### Site

```{r, fig.width=10, fig.height=3}
ranef.plots2[[2]]
```

### Species

```{r, fig.width=4, fig.height=2}
ranef.plots2[[3]]
```

# Model 4

- further remove subject/site random effects to look at species differences (from preregistration)

```{r}
mm.4 <- glmer(correct ~ delay * norm_age +
                task_experience + cup_distance + trial +
                (1 + delay | species)
              , data = model.data
              , family = binomial
              , control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
        )
```

## Random effects

```{r, message=FALSE}
phylo <- read_csv("../data/species_data.csv") %>% 
  select(species, species_formatted, phylo)
```

```{r}
plot.data <- get_model_data(mm.4, type = "re", show.values = T) %>%
  left_join(phylo, by = c("term" = "species")) %>%
  rename(species = species_formatted) %>%
  mutate(
    facet = fct_rev(facet),
    facet = fct_recode(facet, "Intercept" = "species (Intercept)",
                       "Delay (short vs. long)" = "delaylong", 
                       "Delay (short vs. medium)" = "delaymedium")
    )

sorted <- filter(plot.data, facet == "Intercept") %>% arrange(estimate) %>% with(species)
plot.data <- mutate(plot.data, species = factor(species, levels = sorted))
```

```{r, fig.width=6, fig.height=2.5}
re.4 <- ggplot(plot.data, aes(x = species, y = estimate, col = group)) +
  facet_grid(~ facet) +
  geom_hline(yintercept = 1, col = "grey90", size = 1.125) +
  # geom_hline(yintercept = 1, lty = 2) +
  geom_errorbar(aes(ymin = conf.low, ymax = conf.high), width = .3) +
  geom_point(size = 2.5) +
  geom_text(aes(label = p.label), nudge_x = .3, size = 2.5, show.legend = F) +
  scale_y_continuous("Odds Ratios", trans = "log", breaks = c(.1, .2, .5, 1, 2, 5,10,20,40)) +
  scale_colour_brewer(palette = "Set1") +
  coord_flip(ylim = c(.1, 42.5)) + xlab("") +
  guides(col = "none") +
  ggtitle("B. Species Random Effects")
```

```{r, fig.width=8, fig.height=3}
mat <- matrix(c(rep(1, 3), rep(2, 7)), nrow = 1)
grid.arrange(fe.3, re.4, layout_matrix = mat)
```

```{r, warning=FALSE}
ggsave("../graphs/05_forestplot_fe_re.png", arrangeGrob(fe.3, re.4, layout_matrix = mat), width = 8, height = 3, scale = 1.8)

ggsave("../graphs/Fig3.tiff", arrangeGrob(fe.3, re.4, layout_matrix = mat), width = 8, height = 3, scale = 1.8, type = "cairo", compression = "lzw")
```


# Model comparison

We're looking for the lowest AIC(c) as the model with the 'best fit' with a reasonable number of parameters. (Too many are penalized by AIC as one way to address overfitting.)

Indeed, the reduced model seems to do a better job of striking that balance between fitting the data with fewer parameters.

```{r}
AICctab(mm.1, mm.2, mm.3, mm.4, logLik = T, weights = T)
```

```{r}
anova(mm.1, mm.2, mm.3, mm.4)
```

## Difference in regression coefficients

Difference

```{r}
coef1 <- coef(summary(mm.1))[c(2, 3, 6), 1]
coef2 <- coef(summary(mm.3))[c(2, 3, 6), 1]

coef2 - coef1
```

Difference in odds ratios

```{r}
exp(coef2) - exp(coef1)
```

